The EBRD, which invests mainly in the private sector in emerging Europe and North African countries like Egypt, Jordan, Morocco and Tunisia, said the talks were at a very early stage but may culminate this year.
The bank's Kolkata-born president, Sir Suma Chakrabarti, will be following up on the discussions at the World Economic Forum in Davos next week with Tata Group chairman Cyrus Mistry.
"I am looking forward to my meeting with Mr Mistry, who I will be meeting for the first time since he took over as chairman," Suma told reporters at his London headquarters on Friday.
He said: "India has expressed an interest and there are a number of advantages if it were to apply for membership. You don't have to be a member-state for the EBRD to invest but becoming a member would make it natural for the management here to put more effort into our engagement with the Indian government and companies.
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'Secondly, Indian nationals can then become employees of this organisation, which gives Indians the chance of another professional career in another part of the world"..
The EBRD said that 2013 was not an easy one for financing in its regions of operation and that conditions have been tough due to the economic crisis.
However, the bank expects a net profit of 1 billion euros for 2013.
The number of individual projects it has financed stand at 392 in 2013, almost matching the record high of 393 in 2012, according to the bank.